Larmor Frequency

拉莫尔频率

When a magnetic moment is placed in a magnetic field it will tend to align with the field. Classically, a magnetic moment can be visualized as a current loop and the influence toward alignment can be described as the torque on the current loop exerted by the magnetic field. The idea of the magnetic moment as a current loop can be extended to describe the magnetic moments of orbital electrons, electron spins and nuclear spins. In each case the magnetic moment is associated with the angular momentum, and a torque can be identified which tends to align the magnetic moment with the magnetic field. In the nuclear case, the angular momentum involved is the intrinsic angular momentum I associated with the nuclear spin.

当磁矩置于磁场中时，它会倾向于与磁场对齐。经典地，磁矩可以被可视化为一个电流环，磁场对它的作用可以描述为对电流环施加的力矩。将磁矩视为电流环的概念可以扩展到描述轨道电子、电子自旋和核自旋的磁矩。在每种情况下，磁矩都与角动量相关联，并且可以识别出一个力矩，该力矩倾向于使磁矩与磁场对齐。在核的情况下，所涉及的角动量是与核自旋相关的内在角动量I。

When you have a magnetic moment directed at some finite angle with respect to the magnetic field direction, the field will exert a torque on the magnetic moment. This causes it to precess about the magnetic field direction. This is analogous to the precession of a spinning top around the gravity field. The torque can be expressed as the rate of change of the nuclear spin angular momentum I and equated to the expression for the magnetic torque on the magnetic moment

当磁矩与磁场方向成一定角度时，磁场会对磁矩施加力矩。这会导致磁矩围绕磁场方向进动。这类似于陀螺在重力场中的进动。力矩可以表示为核自旋角动量I的变化率，并等于作用在磁矩上的磁力矩的表达式。

which when put in derivative form gives a precession angular velocity

这在导数形式下给出预cession角速度

It can also be visualized quantum mechanically in terms of the quantum energy of transition between the two possible spin states for spin 1/2. This can be expressed as a photon energy according to the Planck relationship. The magnetic potential energy difference is hυ = 2μB. The angular frequency associated with a "spin flip", a resonant absorption or emission involving the spin quantum states is often written in the general form

它也可以从量子力学的角度来可视化，即通过自旋1/2的两个可能自旋态之间的量子能级跃迁来表示。这可以按照普朗克关系表达为光子能量。磁势能差为hυ = 2μB。与自旋翻转相关的角频率，即涉及自旋量子态的共振吸收或发射，通常以一般形式书写。

ω = gB

where g is called the gyromagetic ratio (sometimes the magnetogyric ratio). Note that this frequency is a factor of two higher than the one above because of the spin flip with energy change ΔE = 2μB.

其中，g被称为旋磁比（有时也称为磁旋比）。请注意，这个频率比上面的高两倍，这是因为自旋翻转伴随着能量变化ΔE = 2μB。

This nuclear spin transition for nuclei placed in a magnetic field is the basis for nuclear magnetic resonance (NMR)

这种核自旋在磁场中的转变是核磁共振（NMR）的基础